$K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 8x + 2$ and $ KL = 3x + 27$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {8x + 2} = {3x + 27}$ Solve for $x$ $ 5x = 25$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 8({5}) + 2$ $ KL = 3({5}) + 27$ $ JK = 40 + 2$ $ KL = 15 + 27$ $ JK = 42$ $ KL = 42$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {42} + {42}$ $ JL = 84$